Chapter 25, Problem 1FT

To determine

Utility maximization.

Explanation of Solution

The person’s income is $100 and the person spends all the money to buy a meal, which costs $10 per meal. Thus, the person buys10 $\left(\frac{100}{10}\right)$ meal. The marginal utility deriving from the 10 unit is $5. The price of a movie is $10. Substitute the respective values in Equation (1) to verify whether the person has maximized the utility or not.

$\begin{array}{c}\frac{{\text{Marginal utility}}_{\text{Movie}}}{{\text{Price}}_{\text{Movie}}}=\frac{{\text{Marginal utility}}_{\text{Meal}}}{{\text{Price}}_{\text{Meal}}}\\ \frac{0}{5}=\frac{5}{10}\\ 0<0.5\end{array}$

Since the meal’s marginal utility per dollar is greater than the marginal utility per dollar for the movie, it is concluded that the person did not maximized his utility.

Economics Concept Introduction

Concept Introduction:

Utility maximization: When a person consumes two different goods simultaneously, the person can maximize his or her utility at the point where the marginal utility per dollar derived from both the goods becomes equal. This can be written as follows:

$\frac{{\text{Marginal utility}}_{\text{A}}}{{\text{Price}}_{\text{A}}}=\frac{{\text{Marginal utility}}_{\text{B}}}{{\text{Price}}_{\text{B}}}$ (1)